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  • 1
    Electronic Resource
    Electronic Resource
    Representation of the five-dimensional harmonic oscillator with scalar-valued U(5) &supuline; SO(5) &supuline; SO(3)–coupled VCS wave functions (1995)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 36 (1995), S. 4711-4734 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Vector coherent state methods, which reduce the U(5) &supuline; SO(5) &supuline; SO(3) subgroup chain, are used to construct basis states for the five-dimensional harmonic oscillator. Algorithms are given to calculate matrix elements in this basis. The essential step is the construction of SO(5) &supuline; SO(3) irreps of type [v,0]. The methodology is similar to that used in two recent papers except that one-dimensional, as opposed to multidimensional, vector-valued wave functions are used to give conceptually simpler results. Another significant advance is a canonical resolution of the SO(5) &supuline; SO(3) multiplicity problem. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530915
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Vector coherent state constructions of U(3) symmetric tensors and their SU(3)&supuline;SU(2)×U(1) Wigner coefficients (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2781-2796 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Generalized vector coherent state constructions of totally symmetric U(3) tensors are used to gain new expressions for the SU(3)&supuline;SU(2)×U(1) Wigner coefficients for the coupling (λ1μ1)×(λ20)→(λ3μ3). These expressions show how the extremely simple formulas of Le Blanc and Biedenharn, involving a single 9-j coefficient, arise as special cases of a general result that involves 12-j coefficients. A simpler general result involving only 9-j coefficients and K-normalization factors is derived in a way that can, in principle, be generalized to the generic coupling with multiplicity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528981
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Vector coherent state theory and its application to the orthogonal groups (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 287-304 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Vector coherent state theory is developed and presented in a form that explicitly exhibits its general applicability to the ladder representations of all semisimple Lie groups and their Lie algebras. It is shown that, in a suitable basis, the vector coherent state inner product can be inferred algebraically, by K-matrix theory, and changed to a simpler Bargmann inner product thereby facilitating the explicit calculation of the matrix representaions of Lie algebras. Applications are made to the even and odd orthogonal Lie algebras.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528066
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  • 4
    Electronic Resource
    Electronic Resource
    Symmetries in Nuclei (1973)
    Palo Alto, Calif. : Annual Reviews
    Annual Review of Nuclear and Particle Science 23 (1973), S. 123-161 
    Details
    ISSN: 0066-4243
    Source: Annual Reviews Electronic Back Volume Collection 1932-2001ff
    Topics: Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1146/annurev.ns.23.120173.001011
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  • 5
    Electronic Resource
    Electronic Resource
    A simple class ofU(N) Racah coefficients and their application (1975)
    Springer
    Communications in mathematical physics 41 (1975), S. 135-156 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Using permutation group techniques, a general expression is derived for the special class ofU(N) Racah coefficients for which the representations [f 1] and [f 3] in the recoupling matrix for [f 1]×[f 2]×[f 3]→[f] are either both totally antisymmetric or both totally symmetric. For the totally antisymmetric case further specialization gives a simple expression for aU(N) Racah coefficient which is needed in taking the average of the product of operators over the states of an irreducible representation ofU(N), where this result can be useful in the study of identical fermion systems by spectral distribution methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01608754
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    Paper (German National Licenses)
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